Although we assumed the prior density (REF ), the above makes clear that the result holds for any \(\rho (t)\)  that peaks at sufficiently late times (including the delta function prior (REF ))
such that (REF ) is valid. Thus the above probability distribution is manifestly time-reparametrization invariant. It is also independent of the late-time cutoff, such that the limit \(t_{\rm c}\rightarrow \infty \)  can be taken.
Importantly, the result agrees with the GSVW measure [1]} obtained by counting bubbles along a world-line.GSVW implicitly assumes either that this world-line
survives long enough to probe the asymptotically late-time dynamics, or that their measure is the result of averaging over an ensemble of world-lines such that late-time observers dominate the average.
To be precise, GSVW obtained, working in e-folding time,
\(p_I \sim \sum _j H_j^q \kappa _{Ij} s_j \,.\) 
